### Renormalized entropy solutions of homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic-hyperbolic equations

#### Abstract

We study the well-posedness of renormalized entropy solutions for quasilinear anisotropic degenerate parabolic-hyperbolic equation of the type $\partial_{t}u+\text{div}f(u)=\nabla\cdot(a(u)\nabla u)$ in a bounded domain with general $L^{1}$ initial data and homogeneous Dirichlet boundary condition. We use the device of doubling variables to prove the uniqueness and use the vanishing viscosity method to prove the existence.

#### Article information

Source
Adv. Differential Equations, Volume 19, Number 3/4 (2014), 387-408.

Dates
First available in Project Euclid: 30 January 2014